Airline Overbooking Problem: A small commuter airline charges $100 for tickets on a

Chapter 9, Problem R.8

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Airline Overbooking Problem: A small commuter airline charges $100 for tickets on a particular flight. The plane holds 20 people, so the total revenue for a full flight is $2000. The airline expects a higher revenue by booking 21 passengers and taking their chances that one or more passengers will not show up (the tickets are nonrefundable). Company records indicate that, on average, there is a 10% probability that any one passenger will not show up. However, if everyone does show up, one passenger must be bumped and given a $300 payment. (The $100 is not refunded because the ticket can be used on a later flight.) a. What is the probability that all 21 passengers show up and the airline makes only $1800 ($2100 $300)? What is the probability that 20 or fewer passengers show up and the airline makes the full $2100 on that flight? What is the airlines mathematically expected revenue if it books 21 passengers? b. If the airline books 22 passengers, the revenue is $1600 for zero no-shows, $1900 for one no-show, and $2200 for two or more no-shows. What is the airlines mathematically expected revenue if it books 22 passengers? c. Calculate the mathematically expected revenue if the airline books 23 passengers. Is this more or less than the $2000 it would make if it did no overbooking? d. What other things besides a possible loss of money might make the airline limit the amount of overbooking it does? Weighted Average Problem: For parts e and f, a college professor gives students a weighted average. Test 1 counts as 10% of the grade. Tests 2, 3, and 4 count as 20% each. The final exam counts as 30% of the grade. e. To receive a grade of B or above, a student must have a weighted average of at least 80. Suppose that Nita B. Topaz gets scores of 72, 86, 93, 77, and 98 on the five tests, in that order. Will she get at least a B? Show numbers to support your answer. f. Explain why the mathematics involved in finding a weighted average is the same as that used to find the mathematical expectation of a random experiment.